The final orbit perturbation on our brief list of the most important effects causing changes to orbits is solar radiation pressure (SRP). Like drag, the change is produced by a pressure acting on the spacecraft, but this time the pressure is produced by light, in particular the bright sunshine illuminating the spacecraft. Twentieth century physicists were a clever lot, and they first worked out that light reflecting from a surface exerts a pressure on it. As you read this book, the source of light you are using is producing a small force on the page. The fact that nobody noticed this before the 20th century, suggests that light pressure is tiny, and this is indeed the case. You may recall that the drag force is generated by the impact of air molecules on the spacecraft as it speeds through the atmosphere. SRP shares the same mechanism, but the atmospheric particles are replaced in this case by the stream of particles of light—referred to as photons—emanating from the Sun.

The magnitude of the pressure is unimpressive, amounting to a few millionth of a Newton for every square meter of spacecraft area presented to the Sun. Comparing this with aerodynamic drag, we find that the magnitudes of drag and SRP effects are about the same for a spacecraft in a circular orbit at around a 600- to 700-km (370- to 435-mile) altitude (depending on the level of solar activity; see Chapter 6). There are differences, however; the magnitude of SRP decreases with the distance from the Sun, as opposed to drag, which decreases with increased height above the Earth. Also, the force of SRP generally pushes the spacecraft away from the Sun, whereas the drag force always acts in a retrograde direction with respect to the spacecraft's forward motion.

It is difficult to summarize the effects that SRP have upon the spacecraft orbit in any meaningful way. Below the 600- to 700-km altitude mentioned above, the SRP perturbations are completely swamped by aerodynamic drag. Above this height, the changes they produce are greatly dependent on the aspect that the orbit plane presents to the Sun. The other thing to remember is that the force is tiny. Generally, small cyclic variations in the size, shape, and orbital inclination are produced. But, as we saw with drag, a tiny force acting on the spacecraft in the same way on each orbit over time can accumulate significant orbit changes. Furthermore, if the spacecraft presents a large area to the Sun—for example, solar panels to convert sunlight into usable electrical power—then the perturbing effects on the orbit are further amplified.

One case where the perturbing effects of SRP can be seen to build up, and explained in a fairly intuitive manner, is that of the motion of a satellite in a geostationary Earth orbit (GEO). This is shown as the circle drawn with a continuous line in Figure 3.9a, seen from the perspective of someone looking down from above the Earth's North Pole.

When the spacecraft is at point 1 in the GEO, the SRP force acts in the direction opposing the motion, causing a small decrease in orbital energy. As a consequence, the orbit height achieved on the opposite side of Earth is reduced, thus forming a perigee at point 2. At this point, the SRP force pushes the spacecraft along, tending to produce a small increase in energy that takes the spacecraft to a higher altitude at point 3. The combination of these effects transforms the circular GEO into the elliptic orbit illustrated in Figure 3.9b, which has its major axis aligned at right angles to the direction of the sunlight. As usual, the discussion has been somewhat simplified; for example, the typical eccentricity produced by SRP perturbations in a GEO is generally much less than that shown in Figure 3.9b. Also, it takes many orbit revolutions for the perturbation to build up this moderate eccentricity, rather than the one revolution discussed above. But the message is clear: SRP perturbations increase the eccentricity of a GEO from an initially circular state to an elliptical one. Why is this important?

If you recall the discussion of the GEO orbit in Chapter 2, its main advantage is that a spacecraft in GEO remains stationary with respect to a ground-based observer, so that communications dishes do not have to move to maintain a link. But this is only true if the orbit is circular, when the spacecraft's speed remains constant. If the orbit becomes slightly elliptical, due to the effects of SRP, then the spacecraft moves a little faster than circular orbit speed at the perigee point of the orbit, and a little slower at the apogee point. From the perspective of someone at the ground station, the spacecraft no longer remains stationary at the point where the commu-

Initial GEO orbit Final elliptic orbit

Figure 3.9: The solar radiation pressure perturbation produces an eccentricity in an initially circular orbit.

Initial GEO orbit Final elliptic orbit

Figure 3.9: The solar radiation pressure perturbation produces an eccentricity in an initially circular orbit.

nications dish is directed, but it appears to wander back and forth through this point, with a period of 24 hours. To counter this, the spacecraft again needs to perform orbit control maneuvers to prevent the SRP perturbations building up. The operators of the spacecraft command it to fire small rocket engines (thrusters) to keep the orbit circular. Although light pressure does seem a strange idea, its reality is confirmed by the fact that spacecraft engineers have to estimate an amount of thruster fuel to put in the spacecraft's tanks in order to control its effect on the spacecraft.